We construct a compactification $M^{\mu ss}$ of the Uhlenbeck Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma \colon M^{ss} \to M^{\mu ss}$, where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.

Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces / Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 275:3-4(2013), pp. 1073-1093. [10.1007/s00209-013-1170-9]

Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces

Bruzzo, Ugo;
2013-01-01

Abstract

We construct a compactification $M^{\mu ss}$ of the Uhlenbeck Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma \colon M^{ss} \to M^{\mu ss}$, where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.
2013
275
3-4
1073
1093
10.1007/s00209-013-1170-9
https://arxiv.org/abs/1009.0856
Bruzzo, Ugo; Markushevich, Dimitri; Tikhomirov, Alexander
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15918
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